Image Processing Reference
In-Depth Information
where e is the charge of an electron. The positive and negative charges then move to
the ground plane and to the surface of the photoconductor and discharge the
photoconductor (the polarity depends on the surface charge polarity). By modeling
the photoconductor as a simple capacitor with C as the capacitance per unit area, the
differential discharge per unit area is given by
1
C
ds
d
V
¼
(
10
:
12
)
The negative sign indicates that V decreases as X increases (assuming positive
charging). If the thickness of the photoconductor is L and its dielectric permittivity
is
e
, then C
¼ e=
L. Hence, the PIDC is given by
d
V
d
X
¼
e
C
h(
E
)
(
10
:
13
)
Since the photoconductor can be treated as a simple capacitor with all the
charge residing at the surfaces, the surface voltage V after exposure and the electric
field E are related by V
¼
EL. Using this representation in Equation 10.10, Equation
10.13 becomes
p
V
c
V
V
r
e
h
0
1
þ
d
V
¼
C
d
X
(
10
:
14
)
where V
c
¼
E
c
L
¼a
V
i
with parameter
as a constant and voltage Vi
i
as the initial
voltage on the photoconductor. If the dark decay is zero, then this voltage is same as
the photoconductor surface voltage obtained by Equation 10.6 during the charging
process. The residual voltage V
r
is represented by following expression:
a
L
L
0
V
r
¼
E
r
L
¼
V
r0
(
10
:
15
)
where
L
=
L
0
represents the ratio of the photoconductor thickness to a reference
photoconductor thickness
V
r0
is the residual surface potential under maximum exposure
The ratio L
=
L
0
can be considered equal to one for our purpose. Integrating Equation
10.14 from X
¼
0toX
¼
X, with corresponding values of left integral from Vi
i
to V(X),
we have
p
V
(
X
)
ð
ð
X
0
d
X
¼
e
h
0
C
e
h
0
V
c
V
V
r
1
þ
d
V
¼
C
X
(
10
:
16
)
V
i
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